1、Question:
Tell whether the statement is always, sometimes or never true.
√a + √b = √ab
Correct Answer:To analyze this statement, let us take two examples.
1. a = b = 4
√4 + √4 = √(4 x 4) ?
2 + 2 = √16 ?
4 = 4
The statement is true.
2. a = 9, b = 16
√9 + √16 = √(9 x 16) ?
3 + 4 = √144 ?
7 = 12 ?
The statement is false.
So, the statement √a + √b = √ab is sometimes true.
2、Question:
Tell whether the statement is always, sometimes or never true.
a√b + a√b = 2ab
Correct Answer:To analyze this statement, let us solve the left side of the equation.
a√b + a√b
= 2a√b
2a√b will be equal to 2ab only when √b = b.
This happens only when b = 0 or b = 1. [√0 = 0, √1 = 1]
So, the statement a√b + a√b = 2ab is sometimes true.
Tell whether the statement is always, sometimes or never true.
√a + √b = √ab
Correct Answer:To analyze this statement, let us take two examples.
1. a = b = 4
√4 + √4 = √(4 x 4) ?
2 + 2 = √16 ?
4 = 4
The statement is true.
2. a = 9, b = 16
√9 + √16 = √(9 x 16) ?
3 + 4 = √144 ?
7 = 12 ?
The statement is false.
So, the statement √a + √b = √ab is sometimes true.
2、Question:
Tell whether the statement is always, sometimes or never true.
a√b + a√b = 2ab
Correct Answer:To analyze this statement, let us solve the left side of the equation.
a√b + a√b
= 2a√b
2a√b will be equal to 2ab only when √b = b.
This happens only when b = 0 or b = 1. [√0 = 0, √1 = 1]
So, the statement a√b + a√b = 2ab is sometimes true.